Math Terminology

Question 1

Irrational Numbers

Answer 1

The best known irrational number is the number for Pi π. We are familiar with the idea that 3.14159… goes on to infinity. These kinds of numbers are used in developing theoretical ideas about Mathematical concepts. The test doesn’t go into detail with irrational numbers, but you may see them on the test as part of a question.

Question 2

Rational Numbers

Answer 2

A rational number must be able to be written as a ratio. A ratio is a fraction. A rational number uses whole numbers (0,1, 2, 3…) in the fraction.
 8 is a rational number because we can write it as 8/1
 -8 is not a rational number because we ‘d write as -8/1
Keep in mind that we can write -8/1 but, when we do it’s not rational.

Question 3

Integers

Answer 3

Integers
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
 Examples of integers are: -5 1 5 8 97 and 3,043
 Examples of numbers that are not integers are: -1.43 1 3⁄4 3.14 .09
Think of numbers on a number line going both to the negative side and the positive side. Notice negative numbers are also included but fractions are not.

Question 4

Whole Numbers

Answer 4

Whole Numbers are simply the numbers 0, 1, 2, 3, 4, 5, … (and so on) Notice there are no negative numbers and no fractions.

Question 5

Natural Numbers

Answer 5

The only difference between natural numbers and whole numbers is that a zero is included when mentioning whole numbers. Both natural and whole numbers are positive integers and, therefore, don’t have any fraction or decimal part.

Question 6

Standard Deviation from the Mean

Answer 6

Areyoupanicking? Pushpastthelanguageandfindthemath. Whatisthe everyday definition of the word “mean?” Mean is another way of saying Average. What does “deviation” mean? Different. What does “standard” mean? Typical.
So the standard deviation from the mean is translated as typical difference from the average.

The standard deviation is a measurement statisticians use for the amount ofvariability (or spread) among the numbers in a data set. As the term implies, a standard deviation is a standard (or typical) amount of deviation (or distance) from the average (or mean, as statisticians like to call it). So the standard deviation, in very rough terms, is the average distance from the mean.

Question 7

mean

Answer 7

the average score of all your students.

Question 8

95% of all data points lie within 2 standard deviationsofthe mean. Which of the following assumptions is inherent in the statement?

Answer 8

A. The data are normally distributed.
B. The population is well represented by the data.
C. There are at least 20 data points
D. The data are tightly clustered around the mean.
The answer is A. You know that if the majority of the test scores are only 2 standard deviations of the mean (average) that your test was fair because it is a normal distribution. You probably are familiar with the idea of a“curve” on a test from your college classes or high school experience. Ateacherhastocurvethe test if the standard deviation is too broad. The test wasn’t fair.

Question 9

Don’t use the FORMULA.
It’s not necessary.

Answer 9

All math can be solved by using the most basic Math of Multiply, Divide, Addition and Subtraction. Stay focused and breathe. Push past the language. Find the math you know how to do:
 Find the average of the scores.
 Calculate the difference between each student’s score and the average.
 Square each of those numbers and add them up.
 Find the average of those numbers.
 Then find the square root of the new average.

Question 10

So what do all those symbols mean anyway?
(the formula’s)

Answer 10

Even though you can figure out the answer using simpler math, let’s take a minute to understand what these symbols are all about.
Although ancient Mathematicians were very smart, they were still just regular people. And most people don’t like tedious writing. As a teacher, you don’t feel like writing out: Individualized Education Program every time; so you write IEP. Likewise, ancientGreeksdidn’tfeellikewritingouttheentirewordforthemath terms. So they used abbreviations to make the equation easier to read and faster to write. It also saved paper.

Question 11

Sigma

Answer 11

equivalent to our letter ‘S’. Sigma stands for Sum.

Question 12

Delta (D)

Answer 12

TheGreekwordforDifferenceisDiafora: “Διαφορά”abbreviatedastheletter Delta or D. It looks like this:

Question 13

Pi (P)

Answer 13

P is the symbol for the word “circumference” or “Periphery of a circle.” It is based on the Greek word periféreia “περιφέρεια,”

Question 14

F (statistics)

Answer 14

Function

Question 15

Slope

Answer 15

Rate of Change. The symbol for slope is “m.”
Think of making a stair case as slope. We build stairs by measuring up or down first and then over. How high is each step and how wide is each step? The slope is a number that describes both the direction and the steepness of the line.

When an engineer is making each step they have to figure out how far over (x) and how far up (y) is necessary to make it possible for people to safely walk up
and down the steps. The angle of that steepness is the slope.

Question 16

Positive Slope

Answer 16

“Uphill”

Question 17

Negative Slope

Answer 17

“Downhill”

Question 18

How to solve a slope?

Answer 18

To solve for slope we first do y up or down and then x over

Question 19

Calculus

Answer 19

simply a method “calculating” things we can’t visualize as easily because they are curved.
We rely on the rules of math and formulas to figure out the answer.

Question 20

Quadratic

Answer 20

The name Quadratic comes from “quad” meaning square, because the variable gets squared (like x2).

Question 21

An example of a Quadratic Equation and it’s curve:

Answer 21

5x^2 + 3x + 3

the x^2 makes it quadratic

Question 22

An example of a Quadratic Equation and it’s curve:

Answer 22

5x^2 + 3x + 3

the x^2 makes it quadratic

Question 23

What is a Function?

Answer 23

A function relates an input to an output.
It is like a machine that has an input and an output. And the output is related somehow to the input.

“f(x) = … “ is the classic way of writing a function.

Question 24

Functions: Input, Relationship, Output

Answer 24

In functions there are always three main parts:
 The input
 The relationship
 The output Example: “Multiply by 2” is a very simple function. Here are the three parts:

Question 25

Asymptote

Answer 25

a line that a curve approaches, as it heads towards infinity. It’s a specific type of line used in calculus, but it is still a LINE.

One of the rules involved in calculating an asymptote is that the curve never touches the line. It might look like it’s touching the line but the curve is heading towards infinity, so there will always be a space between the two.

The asymptote is the line. Push past the language and look at the math.
We can solve for the function of x: f(x)
We just need to keep in mind that we’ll use ZERO to figure it out,
since the asymptote never touches the curve.
This is a weird math equation that sounds much harder than it really is.

Question 26

Remember:

Answer 26

All math essentially can be broken down with PEMDAS.

Question 27

Math Advice

Answer 27

During the test, you will be able to access a list of formulas on the screen. But generally, most of the questions can be solved using simple math. This is why we encourage 7-12 test takers to only use the calculator for basic calculations. Using the formulas and the calculator, in ways with which you are not very familiar, can cause confusion and careless mistakes. Keep it SIMPLE.

Flag complicated questions as you go through the test and come back to them after you have answered the easier ones. Do not let the terminology throw you off. Push past the language and find the math.
* Simplify the question as best you can.
* Look at the answers to try to pick up any clues about what they are looking for in the question.
* Then figure out what Math you DO know how to do.
* Use process of elimination.
* Never change your answer unless you are 100% sure it’s wrong.
* Move on. It’s a timed exam.

Remember, you don’t have to get every single answer right. As we explain in the video online, the number you can get wrong depends on the section. But, you can let go of 2 of them guilt free if you are hopelessly confused. Just say, “Ok, that’s one of the one’s I’m getting wrong.”
Pick an answer (never leave an answer blank) and MOVE ON. Come back to it later when you have gotten the rest of the test out of the way. But leave it behind when you are moving on. Don’t let it linger in your brain and distract you on the next question. Keep going. Breathe and focus.

Question 28

Additive Identity Property

Answer 28

The sum of any number and zero is the original number. For example 5 + 0 = 5.

Question 29

Distributive property

Answer 29

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

Question 30

COMMUTATIVE PROPERTY

Answer 30

As teachers we want students to know that what happens on one side of an equation is the same thing that happens on the other. That is what the = sign means. We also want them to know that we can write the numbers in different ways that mean the same thing. So for example:

2 + 3 = 5 can be written 3 + 2 = 5

a x b = c can be written b x a = c

Question 31

Multiplicative Inverse or Reciprocal

Answer 31

Simplified meaning: Inverse or Reciprocal means the OPPOSITE OF.
Just flip it!

Question 32

The Inverse of Adding is Subtracting

Answer 32

Adding moves us one way, subtracting moves us the opposite way.

Question 33

Additive Inverse

Answer 33

what we add to a number to get zero

Question 34

The Inverse of Multiplying is Dividing

Answer 34

Multiplying can be “undone” by dividing.

Question 35

multiplicative inverse

Answer 35

what we multiply a number by to get 1.

Question 36

Dividend

Answer 36

a number to be divided by another number

Question 37

Divisor

Answer 37

a number by which another number is divided

Question 38

Quotient

Answer 38

the number obtained by division

Question 39

Dividend, Divisor, Quotient

Answer 39

Question 40

Mean

Answer 40

“Average”

To find the Mean, add up all the numbers, then divide by how many numbers

Question 41

Median

Answer 41

To find the Median, place the numbers in value order and find the middle number.

Question 42

Mode/Modal Value

Answer 42

To find the Mode, or modal value, place the numbers in value order then count how many of each number. The Mode is the number which appears most often (there can be more than one mode):